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1-4 SOLVING EQUATIONS Properties of Equality Reflexive Property of Equality Symmetric Property of Equality Transitive Property of Equality Substitution

# 1-4 S OLVING E QUATIONS Properties of Equality Reflexive Property of Equality Symmetric Property of Equality Transitive Property of Equality Substitution

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### Text of 1-4 S OLVING E QUATIONS Properties of Equality Reflexive Property of Equality Symmetric Property of... 1-4 SOLVING EQUATIONS

Properties of Equality

Reflexive Property of Equality Symmetric Property of Equality Transitive Property of Equality Substitution PROPERTIES OF EQUALITY

Reflexive Property

• a + b = a + b

The same expression is written on both sides of the equal sign. PROPERTIES OF EQUALITY

• If a = b then b = a

• If 4 + 5 = 9 then 9 = 4 + 5

Symmetric Property PROPERTIES OF EQUALITY

Transitive Property

• If a = b and b = c then a = c

• If 3(3) = 9 and 9 = 4 +5, then 3(3) = 4 + 5 Substitution Property

• If a = b, then a can be replaced by b.

• a(3 + 2) = a(5) NAME THE PROPERTY

• 5(4 + 6) = 20 + 30• 5(4 + 6) = 5(10)• 5(4 + 6) = 5(4 + 6)• If 5(4 + 6) = 5(10) then

5(10) = 5(4 + 6)• 5(4 + 6) = 5(6 + 4)• If 5(10) = 5(4 + 6) and

5(4 + 6) = 20 + 30 then 5(10) = 20 + 30

• Distributive• Substitution• Reflexive• Symmetric

• Commutative• Transitive MORE PROPERTIES OF EQUALITYIF THE OPERATION DONE TO ONE SIDE IS ALSO DONE TO THE OTHER THEN

THE VALUE OF THE EQUATION DOES NOT CHANGE

Addition: If a=b, then a + c = b + c

Subtraction: If a=b, then a – c = b – c

Multiplication: If a=b, then a ∙ c = b ∙ c

Division: If a = b, then a / c = b / c (c≠0)

If x = 12, then x + 3 = 12

+ 3 If x = 12,

then x – 3 = 12 – 3

If x = 12, then x ∙ 3 = 12 ∙

3 If x = 12,

then x / 3 = 12 / 3

Definition Examples SOLVE THE EQUATION

Solving an equation that contains a variable means finding all the possible values that make the equation true. The first step is to isolate the variable to one side of the equation by using inverse operations.

Inverse operations undo operations. Addition, subtraction are inverse operations

as are multiplication, and division . Original equation

Simplify.

Check: Original equation

Simplify.

Substitute 5.5 for s.

Example 1 What is the solution of 12b=18?

12b / 12 = 18 / 12 Divide each side by 12

b = 3 / 2 Simplify Solve

Original equation

Distributive and Substitution Properties

Commutative, Distributive, and Substitution Properties

Division and Substitution Properties What is the solution of -27 + 6y = 3(y – 3)?

-27 + 6y = 3(y – 3) -27 + 6y = 3y – 9 Distributive

Property 6y = 3y + 18 Add 27 to each side. 3y = 18 Subtract 3y from each

side y = 6 Divide each side by

3. What is the solution of 3( 2x – 1) – 2(3x + 4)=11x?

3( 2x – 1) – 2(3x + 4)=11x 6x – 3 – 6x – 8 = 11x Distributive Property – 11 = 11x Combine Like Terms – 1 = x Divide each side by –

11 x = – 1 Symmetric Property   Suppose the flower carpet from Problem 3 had a perimeter of 320 meters. What would the dimensions of the flower carpet be? PROBLEM 4 PAGE 29 PROBLEM #5 PAGE 29 ANOTHER LITERAL EQUATION

Distance = Rate x Time or d = r ∙ t

Solve for r

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